Given $ m \angle AOB = 2x + 22$, $ m \angle BOC = 3x + 14$, and $ m \angle AOC = 71$, find $m\angle AOB$. $O$ $A$ $C$ $B$
Explanation: From the diagram, we see that together ${\angle AOB}$ and ${\angle BOC}$ form ${\angle AOC}$ , so $ {m\angle AOB} + {m\angle BOC} = {m\angle AOC}$ Substitute in the expressions that were given for each measure: $ {2x + 22} + {3x + 14} = {71}$ Combine like terms: $ 5x + 36 = 71$ Subtract $36$ from both sides: $ 5x = 35$ Divide both sides by $5$ to find $x$ $ x = 7$ Substitute $7$ for $x$ in the expression that was given for $m\angle AOB$ $ m\angle AOB = 2({7}) + 22$ Simplify: $ {m\angle AOB = 14 + 22}$ So ${m\angle AOB = 36}$.